Topological investigations of molecular interactions of binary and ternary mixtures containing tetrahydropyran, o-toluidine and N-methylformamide

Thermochimica Acta 524 (2011) 92–103

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Topological investigations of molecular interactions of binary and ternary mixtures containing tetrahydropyran, o-toluidine and N-methylformamide Neeti a , Sunil K. Jangra a , J.S. Yadav b , Dimple c , V.K. Sharma a,∗ a b c

Maharshi Dayanand University, Rohtak, Haryana 124001, India A.I.J.H.M. College, Rohtak 124001, Haryana, India P.D.M. College of Engineering for women, Bahadurgarh, Haryana, India

a r t i c l e

i n f o

Article history: Received 10 April 2011 Received in revised form 28 June 2011 Accepted 29 June 2011 Available online 6 July 2011 Keywords: Excess molar volumes, VE Excess molar enthalpies, HE Excess isentropic compressibilities, SE Connectivity parameter of third degree of a molecule, 3  Interaction parameter, 

a b s t r a c t The densities , speed of sound u, data of o-toluidine (i) + tetrahydropyran (j) + N-methylformamide (k) and its sub-binary o-toluidine (i) + tetrahydropyran (j); tetrahydropyran (j) + N-methylformamide (k); otoluidine (i) + N-methylformamide (k) mixtures have been measured over entire mole fraction at 298.15, 303.15 and 308.15 K. The excess molar enthalpies, HE data of o-toluidine (i) + N-methylformamide (k); tetrahydropyran (j) + N-methylformamide (k) binary mixtures have also been measured as a function of composition at 308.15 K. The densities and speeds of sound of binary and ternary mixtures have been utilized to determine their excess molar volumes, VE and excess isentropic compressibilities, SE . The topology of the constituents (Graph theory) has been employed to determine VE , HE and SE data of binary as well as ternary mixtures. It has been observed that the estimated excess properties compare well with their corresponding experimented values. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Amides are interesting compounds as they possess donor–accepter –CO–NH peptide bond. They also display the property of self-association [1] by hydrogen bond and are related to structural problems in molecular biology. N-methylformamide mainly consists of chain like hydrogen bond structure [2] and has dielectric constant (ε = 182.4) and dipole moment ( = 3.86 D) at 298.15 K. Further, tetrahydropyran is used as solvent in chemical industries in polymerisation processes, pharmaceutical industries as a reaction intermediate [3]. Thus a systematic study of otoluidine (i) or tetrahydropyran (j) + N-methylformamide (k) binary and o-toluidine (i) + tetrahydropyran (j) + N-methylformamide (k) ternary mixtures can provide information about the structural and energy consequence of the interactions between these mixtures. In continuing our study on mixtures containing tetrahydropyran or o-toluidine as one of the component [4–9], we present here densities, speeds of sound data of o-toluidine (i) + tetrahydropyran (j) + N-methylformamide (k) ternary and its sub-binary mixtures over entire composition range at 293.15, 298.15 and 308.15 K. The excess molar enthalpies, HE data of o-toluidine (i) or tetrahy-

∗ Corresponding author. Tel.: +91 9729071881. E-mail address: v [email protected] (V.K. Sharma). 0040-6031/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.tca.2011.06.020

dropyran (j) + N-methylformamide (k) binary mixtures have also been reported as a function of composition at 308.15 K. In recent studies, Graph theory has been successfully employed [4–9] to predict VE , HE and SE data of o-toluidine or tetrahydropyran + aromatic hydrocarbons or cyclo or n-alkane binary mixtures. It would be of interest to see how Graph theory describes the thermodynamic data of the investigated binary and ternary mixture.

2. Experimental o-Toluidine (OT) (Fluka, 0.99 GC), tetrahydropyran (THP) (Fluka, 0.98 GC), N-methylformamide (NMF) (Fluka, 0.98 GC) were purified by standard methods [10]. The purities of the purified liquids were checked by measuring their densities [recorded in Table 1] using Anton Paar DSA 5000 at 298.15 ± 0.01 K and these agreed to within ±2 × 10−3 kg m−3 with their literature values [10–13]. Densities,  and speeds of sound, u of the pure liquids and their binary or ternary mixtures were measured using an Anton Paar vibrating-tube digital density and sound analyzer (model DSA 5000) as explained in the literature [14,15]. The measurements are based on measuring the period of oscillation of a vibrating U-shaped hollow tube filled with the sample. The calibration of the apparatus was carried out with the double distilled, deionized water before each series of measurements. The mole fraction of mixture was

Neeti et al. / Thermochimica Acta 524 (2011) 92–103 Table 1 Comparison of densities,  and speed of sound, u pure liquids with their literature values at a temperature of 298.15 K. /kg m−3

Liquids

o-toluidine Tetrahydropyran N-methylformamide

u/m s−1

Exptl.

Lit.

Exptl.

Lit.

994.351 879.136 999.004

994.30 [10] 879.16 [11] 999.06 [12] 999.00 [13]

1602.57 1269.88 1431.86

1603.0 [4] 1270.0 [16] 1431.21[12] 1431.5 [17]

obtained with uncertainty of 1 × 10−4 from the measured apparent masses of the components. All the mixtures were weighed on an electric balance. The speeds of sound values for the purified liquids at 298.15 ± 0.01 K (recorded in Table 1) compare well with their experimental values [4,12,16,17]. The uncertainties in the density and speeds of sound measurements are 2 × 10−3 kg m−3 and 0.1 m s−1 respectively. Excess molar enthalpies, HE for the binary mixtures were measured by a 2-drop calorimeter (Model, 4600) supplied by the Calorimeter Sciences Corporation (CSC), USA at 308.15 K in a manner described in the literature [4]. The uncertainty in the temperature measurement (in 2-drop calorimeter measured by software provided by CSC; USA) is 0.01 K. The uncertainty in the measured HE value is 1%. Samples for IR studies were prepared by mixing (i) and (j) components in 1:1 (w/w) ratio and their IR spectra were recorded on Perkin Elmer-Spectrum RX-I, FTIR spectrometer.

components were evaluated in the same manner as described elseE ,  , ( ) , E , (E ) where [20]. The resulting V E , Vijk values for S S ijk S S ijk the various binary and ternary are recorded in Tables 2 and 5. The VE , HE and SE data for the binary mixtures (plotted in Figs. 1–3 respectively) were fitted to relation: X E (X = V or H or S ) = xi xj [X (0) + X (1) (2xi − 1) + X (2) (2xj − 1)2 ] (6) where X (n) (X = V or H or S ) etc. are the parameters characteristic of binary mixtures and were determined by fitting XE (X = V or H or S ) data to Eq. (6) using least- squares methods. Such parameters along with standard deviations, (XE ) (X = V or H or S ) are recorded in Tables 2 and 3. E and (E ) The Vijk data for ternary mixtures were fitted to S ijk Redlich–Kister equation



E Xijk (X

= V or S )

k 

VE =

xi Mi ()−1 −

i=i or j

E = Vijk

k 

k 

xi Mi (i )−1

(1)

i=i or j

xi Mi (ijk )−1 −

i=i

k 

xi Mi (i )−1

(2)

i=i

where xi, Mi and i are the mole fraction, molar mass and density of component (i) and , ijk are the densities of binary and ternary mixtures respectively. The isentropic compressibilities, S , (S )ijk and excess isentropic compressibilities SE , (SE )ijk for the investigated binary and ternary mixtures were calculated using equations S = ( u2 )

−1

(S )ijk = (ijk u2ijk ) SE = S − Sid

(3) −1

(4) (5)

Sid values for binary and ternary mixtures were obtained in the manner suggested by Benson and Kiyohara [18]. The Cp,i , i and ˛ values used in Benson and Kiyohara equation represent heat capacity, volume fraction and thermal expansion coefficient of the ith component respectively. The Cp,i values for the pure components were taken from the literature [10,19]. The ˛ value for various

= xi xj

 +xi xk

2 

 (n) (Xij )(xi

− xj )

n

n=0 2 

 + xj xk

(n)

n

 (n) (Xjk )(xj

− xk )

n

n=0

 (Xik )(xk − xj )

2 

 + xi xj xk

n=0

(n)

The Xij

2 

 (7) (n)

n

(Xijk )(xj − xk ) xin

n=0

(n = 0–2) etc. are the adjustable parameters of (i + j), (n)

(j + k), and (i + k) binary mixtures Further, Xijk (X = V or S ) (n = 0–2) etc. are adjustable parameters of the ternary mixtures and were E data to Eq. (7) by least squares determined by fitting the Xijk

E ) method. Such parameters along with standard deviations, (Xijk (X = V or S ) expressed by the relation:

3. Results The densities, ijk , speeds of sound, uijk , data of ternary OT (i) + THP (j) + NMF (k); and densities, , speeds of sound, u of OT (i) + THP (j); THP (j) + NMF (k); OT (i) + NMF (k)of binary mixtures at 298.15, 303.15, 308.15 K; excess molar enthalpies, HE data of OT (i) or THP (j) + NMF (k) mixtures over entire composition at 308.15 K are recorded in Tables 2–4 respectively. Excess molar volumes E for various binary and ternary mixtures were determined V E , Vijk from their measured density data using

93

E )= (Xijk

⎧  2 ⎫0.5

E ⎪ ⎪ E ⎨ ⎬ Xijk − Xijk{calc. Eq. (7 ) } ⎪ ⎩

(m − n)

⎪ ⎭

(8)

where m is the number of data points and n is the number of adjustable parameters of Eq. (7) are recorded in Tables 2 and 3 E and (E ) respectively. The various surfaces generated by Vijk ijk values [calculated via Eq. (7)] for OT (i) + THP (j) + NMF (k) ternary mixtures are shown in Figs. 4–9 respectively. Figs. 4–9 are plotted E and (E ) by calculating Vijk values from Eq. (7) keeping the mole S ijk fraction of the one component constant and varying the other mole E values fractions. In Fig. 4, keeping mole fraction of xj constant Vijk (corresponding to i–k axis) were calculated and are represented by E values (corresponding to i–j axis) were obtained ( ). The Vijk

E keeping xk constant and varying the values of xi and xj . Such Vijk values are shown as ( ).

4. Discussion The VE values for THP + NMF binary mixture have been reported in literature at 298.15, 303.15, 308.15 K, our VE values differ by 0.003 cm3 mol−1 than those reported in literature [13], Further, our VE values for OT (i) + THP (j) binary mixture are in excellent agreement with values reported in literature at 308.15 K. We are unaware of the VE data of the remaining binary and ternary mixtures,; HE and SE data of the investigated binary and SE data of the studied ternary mixtures with which to compare our results. The VE data of binary OT (i) + THP (j); THP (j) + NMF (k); OT (i) + NMF (k) and HE , SE values of OT (i) + NMF (k) binary mixtures are negative over entire range of composition. However, HE and SE values of THP (j) + NMF (k) mixtures are positive over whole mole fraction. Further, VE and SE data of the investigated ternary mixtures are negative over entire composition range. The HE data of OT (i) or THP (j) + NMF (k) mixtures can be explained qualitatively, if it is assumed that (i) OT (i) or THP (j)

94

Neeti et al. / Thermochimica Acta 524 (2011) 92–103

Table 2 Measured densities, ; excess molar volumes, VE ; speeds of sound, u; isentropic compressibilities, S and excess isentropic compressibilities, SE data for the various binary mixtures as a function of mole fraction, xi , of component (i) at a temperature of 298.15, 303.15 and 308.15 K. xi

/kg m3

o-toluidine (i) + tetrahydropyran (j) T = 298.15 Ka 0.0 879.136 890.691 0.0732 899.769 0.1342 905.846 0.1768 0.2207 911.867 0.2721 918.660 926.351 0.3328 929.219 0.3562 933.275 0.3901 937.818 0.4288 0.4567 940.995 0.5014 945.986 0.5362 949.788 956.336 0.5982 0.6243 959.040 0.6644 963.103 967.870 0.7125 973.454 0.7703 976.501 0.8025 1.0 994.351 303.15 Kb 0.0000 873.992 0.0732 885.730 894.897 0.1342 900.991 0.1768 907.057 0.2207 0.2721 913.860 0.3328 921.578 0.3562 924.445 0.3901 928.536 933.094 0.4288 936.325 0.4567 941.370 0.5014 0.5362 945.194 0.5982 951.867 0.6243 954.607 0.6644 958.737 963.596 0.7125 969.292 0.7703 972.384 0.8025 1.0 990.224 308.15 Kc 0.0 868.831 0.0732 880.749 890.021 0.1342 896.174 0.1768 902.258 0.2207 909.112 0.2721 916.872 0.3328 919.758 0.3562 923.890 0.3901 928.469 0.4288 931.715 0.4567 936.823 0.5014 940.693 0.5362 947.455 0.5982 950.235 0.6243 954.427 0.6644 959.361 0.7125 965.131 0.7703 968.276 0.8025 986.069 1.0 o-toluidine (i) + N-methylformamide (k) T = 298.15 Kd 0.0 999.004 1000.18 0.0656 1000.98 0.1258 0.1673 1001.39 0.2127 1001.71 1001.88 0.2466 0.2789 1001.99 1002.03 0.3081 0.3356 1002.04

VE /cm3 mol−1

u/m s−1

S /TPa−1

SE /TPa−1

– −0.2594 −0.4242 −0.5156 −0.5881 −0.6510 −0.6978 −0.7078 −0.7139 −0.7148 −0.7072 −0.6882 −0.6678 −0.6141 −0.5886 −0.5426 −0.4807 −0.3977 −0.3478 –

1269.88 1296.39 1318.61 1333.98 1349.85 1368.16 1389.27 1397.33 1408.97 1421.78 1430.96 1445.54 1456.56 1475.66 1483.59 1495.66 1510.15 1527.40 1537.04 1602.57

– 668.04 639.20 620.36 601.86 581.53 559.30 551.17 539.74 527.49 518.99 505.89 496.27 480.19 473.74 464.15 453.05 440.33 433.47 –

– −14.36 −24.06 −29.53 −34.26 −38.46 −41.64 −42.43 −43.22 −43.33 −43.08 −42.15 −40.85 −37.47 −35.74 −32.74 −28.75 −23.33 −20.09 –

– −0.2754 −0.4454 −0.5352 −0.6087 −0.6678 −0.7113 −0.7187 −0.7249 −0.7232 −0.7182 −0.6998 −0.6776 −0.6299 −0.605 −0.5611 −0.5031 −0.4248 −0.3755 –

1246.83 1274.12 1296.85 1312.52 1328.63 1347.13 1368.74 1376.92 1388.49 1401.63 1411.09 1425.65 1437.04 1456.47 1464.71 1476.95 1491.34 1508.67 1518.08 1577.82

– 695.47 664.43 644.27 624.53 602.98 579.21 570.56 558.62 545.52 536.37 522.65 512.32 495.24 488.28 478.16 466.61 453.27 446.24 –

– −16.35 −27.24 −33.32 −38.56 −43.13 −46.86 −47.77 −48.51 −48.83 −48.76 −47.71 −46.55 −43.14 −41.48 −38.36 −34.02 −28.26 −24.65 –

– −0.2915 −0.4688 −0.5617 −0.6332 −0.6930 −0.7349 −0.7418 −0.7488 −0.7451 −0.7386 −0.7219 −0.7005 −0.6549 −0.6311 −0.5891 −0.5330 −0.4553 −0.4076 –

1224.47 1252.49 1275.85 1291.97 1308.47 1327.61 1349.47 1357.79 1369.76 1383.06 1392.32 1407.17 1418.24 1437.56 1445.68 1457.60 1471.77 1488.59 1497.88 1558.38

– 723.77 690.24 668.51 647.36 624.09 598.91 589.74 576.89 563.06 553.65 539.07 528.51 510.73 503.53 493.15 481.21 467.59 460.31 –

– −18.26 −30.44 −37.26 −43.04 −48.31 −52.24 −53.22 −54.21 −54.49 −54.13 −53.06 −51.44 −47.52 −45.58 −41.92 −37.02 −30.41 −26.42 –

– −0.1063 −0.1914 −0.2439 −0.2935 −0.3268 −0.3556 −0.3772 −0.3957

1431.86 1454.27 1472.38 1484.06 1496.05 1504.40 1512.07 1518.62 1524.41

– 472.75 460.82 453.41 446.03 441.02 436.51 432.74 429.45

– −8.51 −14.66 −18.09 −21.11 −22.87 −24.28 −25.25 −25.90

Neeti et al. / Thermochimica Acta 524 (2011) 92–103

95

Table 2 (Continued ) xi

/kg m3

0.3898 1001.96 0.4383 1001.79 0.4802 1001.56 1001.25 0.5269 1000.97 0.5599 1000.59 0.6006 1000.02 0.6519 0.7244 999.105 0.7904 998.148 0.8485 997.204 994.351 1.0 303.15 Ke 0.0 994.653 0.0656 995.882 0.1258 996.704 0.1673 997.124 0.2127 997.464 0.2466 997.650 0.2789 997.753 0.3081 997.811 997.839 0.3356 997.768 0.3898 997.624 0.4383 0.4802 997.416 0.5269 997.104 0.5599 996.843 0.6006 996.484 995.935 0.6519 995.043 0.7244 994.083 0.7904 0.8485 993.140 1.0 990.224 308.15 Kf 0.0 990.302 991.550 0.0656 0.1258 992.418 0.1673 992.870 0.2127 993.254 0.2466 993.459 993.588 0.2789 993.675 0.3081 993.709 0.3356 0.3898 993.664 0.4383 993.525 0.4802 993.334 0.5269 993.020 992.760 0.5599 992.392 0.6006 991.837 0.6519 990.907 0.7244 989.937 0.7904 988.977 0.8485 986.069 1.0 Tetrahydropyran (j) + N-methylformamide (k) T = 298.15 Kg 0.0 999.004 984.359 0.0822 971.886 0.1587 960.487 0.2344 0.2633 956.359 0.3005 951.208 943.711 0.3572 940.623 0.3814 936.288 0.4163 0.4334 934.212 0.4851 928.124 925.036 0.5122 918.752 0.5693 914.817 0.6064 909.625 0.6571 905.507 0.6988 902.361 0.7315 898.361 0.7743 891.856 0.8468 1.0 879.136 303.15 Kh 0.0 994.653

VE /cm3 mol−1

u/m s−1

S /TPa−1

SE /TPa−1

−0.4245 −0.4428 −0.4503 −0.4533 −0.4492 −0.4405 −0.4190 −0.3726 −0.3129 −0.2451 –

1535.19 1543.96 1551.07 1558.20 1562.89 1568.18 1574.36 1582.15 1588.23 1592.85 1602.60

423.48 418.74 415.01 411.35 409.01 406.40 403.44 399.84 397.17 395.24 –

−26.67 −26.75 −26.46 −25.64 −24.82 −23.52 −21.55 −18.19 −14.53 −10.88 –

– −0.1087 −0.1951 −0.2475 −0.2984 −0.3326 −0.3603 −0.3831 −0.4026 −0.4315 −0.4505 −0.4596 −0.4618 −0.4591 −0.4512 −0.4305 −0.3855 −0.3244 −0.2555 –

1417.66 1438.44 1456.30 1467.84 1479.70 1488.16 1495.69 1502.34 1508.21 1518.88 1527.61 1534.6 1541.45 1545.93 1551.11 1556.65 1563.43 1568.28 1571.88 1577.82

– 485.31 473.08 465.47 457.89 452.61 448.01 444.03 440.57 434.43 429.55 425.73 422.08 419.75 417.11 414.37 411.15 409.01 407.52 –

– −8.74 −15.27 −18.95 −22.24 −24.31 −25.85 −27.07 −27.93 −28.94 −29.24 −29.09 −28.32 −27.53 −26.32 −24.21 −20.57 −16.47 −12.46 –

– −0.1094 −0.1984 −0.2527 −0.3064 −0.3417 −0.3711 −0.3958 −0.4157 −0.4463 −0.4655 −0.4756 −0.4774 −0.4744 −0.4654 −0.4435 −0.3938 −0.3305 −0.2586 –

1402.55 1423.32 1440.91 1452.23 1463.85 1471.94 1479.40 1485.71 1491.39 1501.86 1510.38 1517.25 1524.11 1528.45 1533.61 1539.19 1545.99 1550.91 1554.24 1558.38

– 497.83 485.32 477.57 469.83 464.59 459.86 455.92 452.44 446.17 441.21 437.31 433.52 431.17 428.44 425.57 422.23 419.97 418.58 –

– −9.22 −15.96 −19.74 −23.13 −25.13 −26.77 −27.91 −28.76 −29.84 −30.15 −30.04 −29.36 −28.55 −27.39 −25.34 −21.74 −17.68 −13.51 –

– −0.0531 −0.0952 −0.1289 −0.1397 −0.1515 −0.1666 −0.1714 −0.1767 −0.1787 −0.1824 −0.1826 −0.1795 −0.1745 −0.1647 −0.1541 −0.1434 −0.1276 −0.0944 –

1431.86 1411.82 1394.05 1377.93 1372.11 1364.96 1354.53 1350.33 1344.43 1341.60 1333.40 1329.29 1321.01 1315.89 1309.14 1303.83 1299.83 1294.70 1286.41 1269.88

509.67 529.45 548.34 555.41 564.27 577.54 583.05 590.90 594.72 606.01 611.79 623.73 631.29 641.45 649.63 655.91 664.06 677.56 –

4.21 7.33 9.73 10.49 11.26 12.18 12.42 12.67 12.76 12.78 12.67 12.17 11.65 10.77 9.86 9.02 7.85 5.56 –

–

1417.66

–

–

96

Neeti et al. / Thermochimica Acta 524 (2011) 92–103

Table 2 (Continued ) xi

/kg m3

VE /cm3 mol−1

u/m s−1

S /TPa−1

SE /TPa−1

0.0822 0.1587 0.2344 0.2633 0.3005 0.3572 0.3814 0.4163 0.4334 0.4851 0.5122 0.5693 0.6064 0.6571 0.6988 0.7315 0.7743 0.8468 1.0 308.15 Ki 0.0 0.0822 0.1587 0.2344 0.2633 0.3005 0.3572 0.3814 0.4163 0.4334 0.4851 0.5122 0.5693 0.6064 0.6571 0.6988 0.7315 0.7743 0.8468 1.0

979.949 967.407 955.945 951.788 946.607 939.057 935.944 931.584 929.494 923.354 920.247 913.910 909.949 904.722 900.569 897.401 893.366 886.811 873.992

−0.0577 −0.1024 −0.1385 −0.1496 −0.1623 −0.1779 −0.1825 −0.1884 −0.1904 −0.1934 −0.1938 −0.1897 −0.1845 −0.1744 −0.1627 −0.1515 −0.1344 −0.0993 –

1396.37 1377.92 1361.03 1354.95 1347.37 1336.47 1332.02 1325.82 1322.87 1314.31 1310.01 1301.35 1295.98 1288.96 1283.45 1279.26 1273.89 1265.07 1246.83

523.36 544.43 564.72 572.29 581.91 596.20 602.19 610.67 614.78 626.96 633.22 646.11 654.32 665.28 674.11 680.92 689.77 704.59 –

3.73 6.77 9.21 9.97 10.82 11.74 12.02 12.28 12.36 12.35 12.22 11.65 11.11 10.12 9.11 8.22 6.98 4.71 –

990.302 975.601 963.009 951.454 947.263 942.041 934.409 931.277 926.867 924.763 918.566 915.428 909.049 905.053 899.790 895.605 892.421 888.365 881.763 868.831

– −0.0664 −0.1157 −0.1524 −0.1637 −0.1766 −0.1906 −0.1956 −0.2001 −0.2023 −0.2041 −0.2037 −0.1995 −0.1935 −0.1829 −0.1704 −0.1595 −0.1423 −0.1058 –

1402.55 1380.66 1361.68 1344.41 1338.11 1330.33 1319.09 1314.46 1308.04 1304.99 1296.11 1291.60 1282.56 1276.98 1269.56 1263.71 1259.26 1253.53 1244.09 1224.47

– 537.71 560.04 581.51 589.58 599.81 615.06 621.48 630.58 634.98 648.05 654.82 668.74 677.57 689.53 699.17 706.64 716.38 732.73 –

– 3.48 6.35 8.56 9.29 10.05 10.88 11.15 11.37 11.42 11.35 11.22 10.62 10.02 9.08 8.12 7.27 6.12 4.03 –

a b

V(0) = −2.7547; V(1) = 1.0670; V(2) = −0.2148; (VE ) = 0.0006 cm3 mol−1 S = −168.56; S = 61.44; S = 12.40; (SE ) = 0.03 TPa−1 . (0)

(1)

(2)

V(0) = −2.7991; V(1) = 1.0246; V(2) = −0.5254; (VE ) = 0.0007 cm3 mol−1 S = −191.22; S = 58.69; S = 0.06; (SE ) = 0.04 TPa−1 . (0)

(0)

= −2.8877; V

c

(1)

V

d

V(0) = −1.8101; V(1)

e

V(0) = −1.8456; V(1)

f

V(0) = −1.9095; V(1)

g

V(0) = −0.7302; V(1)

h

V(0) = −0.7747; V(1)

i

V(0) = −0.8168; V(1)

(1)

(2)

(0) (1) (2) = 0.9953; V = −0.7740; (V ) = 0.0007 cm mol S = −121.21; S = 71.43; S = 5.19; (SE ) = 0.05 TPa−1 . (0) (1) (2) = −0.1140; V(2) = −0.0324; (VE ) = 0.0004 cm3 mol−1 S = −104.53; S = 33.27; S = −7.02; (SE ) = 0.02 TPa−1 . (0) (1) (2) = −0.1521; V(2) = −0.0780; (VE ) = 0.0004 cm3 mol−1 S = −115.28; S = 28.89; S = −3.12; (SE ) = 0.02 TPa−1 . (2) (2) (2) E 3 −1 (0) = −0.1432; V = −0.0021; (V ) = 0.0004 cm mol S = −119.11; S = 27.04; S = −10.06; (SE ) = 0.03 TPa−1 . (0) (1) (2) = -0.0115; V(2) = −0.0233; (VE ) = 0.0001 cm3 mol−1 S = 50.87; S = −8.62; S = −4.20; (SE ) = 0.01 TPa−1 . (1) (2) (2) E 3 −1 (0) = 0.0021; V = 0.0127; (V ) = 0.0002 cm mol S = 49.22; S = −10.22; S = −12.02; (SE ) = 0.01 TPa−1 . (0) (1) (2) = −0.356; V(2) = 0.0509; (VE ) = 0.0002 cm3 mol−1 S = 45.15; S = −11.63; S = −12.59; (SE ) = 0.01 TPa−1 . (2)

E

3

−1

or NMF (k) are associated molecular entities, (ii) there is interaction between THP or OT with NMF; (iii) interactions between THP or OT with NMF leads to their depolymerisation to form their respective monomers; and (iv) monomers of OT or THP or NMF undergo interactions to form 1:1 molecular complex. The HE data of THP (j) + NMF (k) mixtures suggest that contribution due to factor (iii) far outweigh the contribution due to factors (ii) and (iv) so that overall HE values for this are positive. However, HE data of OT (i) + NMF (k) mixtures suggest that contribution due to factors (ii) and (iv) is more significant as compared to factor (iii). Further, VE and SE data of these mixtures suggest that OT gives relatively more packed structure in NMF as compared to THP. This may be due to strong interactions between OT (i) and NMF (k) as compared to THP. E and (E ) The Vijk data of OT (i) + THP (j) + NMF (k) mixture are S ijk negative over entire composition range and suggest that addition of NMF (k) to OT (i) + THP (j) mixture gives relatively more packed structure and strong interactions in mixed state as compared to

pure state. Further decrease in speed of sound values with increase in temperature lends additional supports to this view point.

5. Graph theory 5.1. Excess molar volumes of binary mixtures The VE reflects packing effect (which in turn depends on the topology of (i)/(j)/(k)) and as topology of the components (i)/(j)/(k) changes in (i + j) or (j + k) mixtures, it was therefore worthwhile to analyze VE data of (i + j) or (j + k) mixtures in terms of Graph theory. This theory deals with connectivity parameter of third degree, 3  of a molecule (which depends upon its topology). According to Graph theory (21) E

V =˛

 

3

xi ( i )m

−1

−



3

−1 

xi ( i )

(9)

Neeti et al. / Thermochimica Acta 524 (2011) 92–103

97

Table 3 Measured excess molar enthalpies, HE values for the various binary mixtures as a function of mole fraction xi , of component (i) at a temperature of 308.15K. HE /J mol−1

xi

xi

HE /J mol−1

a

o-toluidine (i) + N-methyl formamide (k) 0.0486 −168.1 0.4811 0.0972 −313.2 0.5306 −420.8 0.5822 0.1358 −527.6 0.6225 0.1888 −606.5 0.6788 0.2267 0.7121 0.2786 −668.5 0.3432 −730.2 0.7826 −761.4 0.8127 0.3972 −765.1 0.8455 0.4209 Tetrahydropyran (j) + N-methyl formamide (k)b 0.0662 34.1 0.5562 0.1805 122.4 0.5923 155.6 0.6242 0.2254 0.6675 0.2892 206.1 236.1 0.7153 0.3252 0.3743 267.9 0.7576 278.8 0.7901 0.4016 313.5 0.8152 0.4724 323.1 0.8676 0.5114 a b

−756.3 −732.1 −679.1 −638.5 −578.4 −519.3 −404.4 −358.9 −298.1 326.6 324.5 312.6 304.2 275.5 252.1 223.2 201.7 153.7

Fig. 2. Excess isentropic compressibilities, SE for tetrahydropyran (j) + N-methyl formamide (k) (I) 308.15 K Exptl. (

H(0) = −2978; H(1) = 915.4; H(2) = 174.7; (HE ) = 6.5 J mol−1 . H(0) = 1270.6; H(1) = 418.9; H(2) = −465.8; (HE ) = 2.5 J mol−1 .

),Graph ; (III) 308.15 K Exptl. ( formamide (k) (IV) 298.15 K Exptl. (

) Graph

; (II) 303.15 K Exptl. (

),Graph ; o-toluidine (i) + N-methyl ), Graph ; (V) 303.15 K Exptl.

( ) Graph ; (VI) 308.15 K Exptl. ( (i) + tetrahydropyran (j) (VII) Exptl. (—); (VIII) Exptl. ( ).

), Graph ; o-toluidine ); (IX) Exptl. (

Fig. 1. Excess molar volumes, VE for tetrahydropyran (j) + N-methyl formamide (k) at (I) 298.15 K Exptl. ( (III) 308.15 K Exptl. ( (IV) 298.15 Exptl. (

), Graph

; (II) 303.15 K Exptl. (

),Graph

;

),Graph ; o-toluidine (i) + N-methyl formamide (k) )Graph ; (V) 303.15 Exptl. ( ),Graph ; (VI)

308.15 Exptl. ( ),Graph ); (VIII) Exptl. ( (

; o-toluidine (i) + tetrahydropyran (j) (VII) Exptl. ); (IX) Exptl. ( ).

Fig. 3. Excess molar enthalpies, HE for tetrahydropyran (j) + N-methyl formamide ) Graph ; (II); o-toluidine (i) + N-methyl formamide (k) (I) 308.15 K Exptl. ( (k) (IV) 308.15 K Exptl. (

where ˛ is a constant characteristic of (i + j), (j + k) mixtures. The 3  i , (3  i )m (i = i or j or k) are connectively parameters of third degree in pure and mixed state defined by [21] 3

=



(ı m ı n ı o ı p )

−0.5

(10)

m
where ı m etc. have the same significance as described in the literature [22]. The 3  etc. parameters were determined by fitting experiments VE data to Eq. (9) and only those values of 3  etc. parameters were retained that best reproduced the experimental VE values. Such 3  i (i = i or j or k), (3  i )m (i = i or j or k) parameter along with the VE values [calculated via Eq. (9)] at various mole fraction of component (i), xi are recorded in Table 4. Examination of data in Table 4 suggests that VE values compare well with experimental values. The 3  etc. parameters values were therefore utilized to extract information about the state of components (i)/(j)/(k) in their pure and

), Graph

.

mixed state. For this purpose numbers of structures were assumed for OT, THP, NMF (Scheme 1) and their 3 /values were calculated from structural consideration [using Eq. (10)]. These 3 / values were compared with 3  values [determined via Eq. (9)]. Any structure or combination of structures that provided 3 / value which compare with 3  value was taken to be representative structure of that component. Such an analysis revealed that OT (molecular entities I–II; 3 / = 0.949, 1.405 3  = 1.202); THP (molecular entities III–IV; 3  = 1.078, 1.349, 3  = 1.301), NMF (molecular entities V–VI; 3 / = 0.236, 0.947, 3  = 0.890) exits as associated molecular entities; II, IV and VI respectively. The information about the state of OT (i) or THP (j) in (i + j) or / (j + k) mixtures was obtained by predicting (3 i )m (i = i or j) values. For this purpose it was assumed that studied mixtures may have molecular entities VII and VIII respectively. While molecular entity VII is assumed to be characterized by interactions between oxy-

98

Neeti et al. / Thermochimica Acta 524 (2011) 92–103

Scheme 1. Connectivity parameters of third degree, 3  / , for various molecular entities.

gen atom of THP with hydrogen atom of NMF; molecular entity VIII is characterized by interactions between hydrogen atom of / OT and oxygen atom of NMF. The (3 i )m (i = i or j) values for these molecular entities were then calculated to be 1.142, 1.505 respectively. The (3 i )m (i = i or j) value of 1.201, 1.301 (Table 4) suggests the presence of molecular entities VII, VIII in the investigated mixtures. The existence of molecular entities VII, VIII in

the mixtures suggest that addition of NMF (k) to OT(i) or THP (j) must change the C–O–C vibrations of THP; N–H vibrations of OT; and C O vibrations of NMF. The IR spectral data were, therefore, analyzed for pure OT, THP, NMF and their equimolar OT (i) or THP (j) + NMF (k) binary mixtures. It was observed that characteristic (C–O–C) vibration at 1090 cm−1 in pure [23] THP (j) shifted to 1110 cm−1 ; (N–H stretching) at 3471, 3366 cm−1 (sym-

Neeti et al. / Thermochimica Acta 524 (2011) 92–103

99

Table 4 Comparison of calculated VE , HE (at T = 308.15 K) and SE values from appropriate equations with their corresponding experimental values at temperature of (298.15, 303.15 /

and 308.15) K along with their (3  i ) = (3  j )m (i = i or j); ˛ij ik or jk and ij parameters for the various binary mixtures as a function of xi , mole fraction of component (i). Properties

Mole fraction of component (i), xi 0.1

0.2

o-toluidine (i) + N-methylformamide (k) 298.15 Ka VE (Exptl.) −0.1565 −0.2805 −0.1850 −0.3181 VE (Graph) −12.21 −20.31 SE (Exptl.) SE (Graph) −11.59 −19.73 303.15 Kb VE (Exptl.) −0.1597 −0.2852 −0.1886 −0.3243 VE (Graph) E −12.64 −21.40 S (Exptl.) SE (Graph) −12.26 −21.03 308.15 Kc VE (Exptl.) −0.1614 −0.2965 VE (Graph) −0.1951 −0.3356 HE (Exptl.) −324.1 −554.5 E H (Graph) −326.8 −556.9 SE (Exptl) −13.25 −22.23 SE (Graph) −12.51 −21.53 Tetrahydropyran (j) + N-methylformamide (k) 298.15 Kd VE (Exptl.) −0.0635 −0.1144 VE (Graph) −0.0773 −0.1317 E 4.96 8.72 S (Exptl.) E S (Graph) 5.11 8.87 303.15 Ke VE (Exptl.) −0.0689 −0.1231 −0.0820 −0.1397 VE (Graph) 4.47 8.16 SE (Exptl.) SE (Graph) 5.03 8.69 f 308.15 K E V (Exptl.) −0.0791 −0.1370 −0.0865 −0.1473 VE (Graph) 57.0 136.3 HE (Exptl.) HE (Graph) 86.2 163.8 4.18 7.61 SE (Exptl.) SE (Graph) 4.75 8.15

0.3

0.4

0.5

0.6

0.7

0.8

0.9

−0.3716 −0.4042 −24.98 −24.69

−0.4293 −0.4478 −26.75 –

−0.4525 − −26.13 −26.25

−0.4402 −0.4218 −23.55 –

−0.3908 −0.3587 −19.39 −19.07

−0.3025 −0.2658 −13.94 −13.29

−0.1730 −0.1455 −7.42 −6.73

−0.3774 −0.4122 −26.74 −26.56

−0.4364 −0.4566 −29.08 –

−0.4614 − −28.82 −28.89

−0.4510 −0.4301 −26.31 –

−0.4030 −0.3658 −21.89 −21.69

−0.3144 −0.2710 −15.85 −15.45

−0.1816 −0.1484 −8.48 −8.04

−0.3889 −0.4265 −696.6 −697.7 −27.62 −27.27

−0.4514 −0.4724 −757.2 – −29.98 −29.98

−0.4774 −0.4774 −744.8 −744.4 −29.77 −29.92

−0.4651 −0.4450 −669.4 – −27.38 −27.38

−0.4130 −0.3784 −542.8 −543.6 −23.08 −22.71

−0.3192 −0.2804 −378.7 −380.1 −17.04 −16.29

−0.1821 −0.1535 −192.2 −193.3 −9.35 −8.56

−0.1516 −0.1658 11.27 11.33

−0.1745 −0.1821 12.58 –

−0.1826 − 12.72 12.67

−0.1756 −0.1690 11.75 –

−0.1535 −0.1427 9.82 9.87

−0.1166 −0.1050 7.07 7.19

−0.0652 −0.0572 3.72 3.84

−0.1623 −0.1759 10.79 11.05

−0.1859 −0.1932 12.19 −

−0.1937 – 12.30 12.21

−0.1858 −0.1792 11.21 −

−0.1621 −0.1514 9.07 9.33

−0.1231 −0.1114 6.20 6.71

−0.0687 −0.0606 3.00 3.53

−0.1762 −0.1854 216.1 229.6 10.03 10.30

−0.1982 −0.2037 280.4 – 11.27 –

−0.2042 − 317.7 312.2 11.28 11.18

−0.1948 −0.1889 320.6 – 10.16 –

−0.1702 −0.1596 286.4 300.3 8.08 8.34

−0.1302 −0.1175 216.7 245.1 5.38 5.91

−0.0739 −0.0639 117.7 147.0 2.50 3.05

a

(3  i ) = (3  i )m = 1.202; (3  k ) = (3  k )m = 0.890; ˛ik = 20.8063 cm3 mol−1 ; ik = 66.99 TPa−1 ; * = 9.11 TPa−1 .

b

(3  i ) = (3  i )m = 1.202; (3  k ) = (3  k )m = 0.890; ˛ik = 21.2156 cm3 mol−1 ; ik = −70.33 TPa−1 ; * = 4.92 TPa−1 .

/

/

3

3

3

3

3

−1

−1

/

; ik = −1886.4 Jmol

; * = 238.4 J mol−1 ; ik = −71.60 TPa−1 ; ␹* = 3.28 TPa−1 .

c

(  i ) = (  i )m = 1.202; (  k ) = (  k )m = 0.890; ˛ik = 21.9513 cm mol

d

(3  j ) = (3  j )m = 1.301; (3  k ) = (3  k )m = 0.890; ˛jk = 5.4848 cm3 mol−1 ; jk = 29.01 TPa−1 ; * = −0.78 TPa−1 .

e

(3  j ) = (3  j )m = 1.301; (3  k ) = (3  k )m = 0.890; ˛jk = 5.8182 cm3 mol−1 ; jk = 28.71 TPa−1 ; * = −1.94 TPa−1 .

f

(3  j ) = (3  j )m = 1.301; (3  k ) = (3  k )m = 0.890; ˛jk = 6.1336 cm3 mol−1 ; jk = 448.42Jmol

/

/ / /

−1

; * = 379.04 J mol−1 ; jk = 27.23 TPa−1 ; * = −3.17 TPa−1 . /

metric and asymmetric vibrations) in pure OT (i) shifted to 3449, 3350 cm−1 ; and (C O) vibrations at 1670 cm−1 in pure NMF shifted to 1655 cm−1 in mixed state. The IR spectral data of the mixtures thus reveals that addition of NMF (k) to OT(i) or THP (j) influence the (C–O–C stretching), (N–H stretching), (C O) vibrations of THP, OT, NMF which in turn lends additional support to the presence of molecular entities VII, VIII in OT(i) or THP (j) + NMF (k) mixtures.

5.2. Excess molar enthalpies and excess isentropic compressibilities of binary mixtures

E Fig. 4. Excess molar volumes, Vijk , for o-toluidine (i) + tetrahydropyran (j) + N-

methyl formamide (k) ternary mixture at 298.15 K, , the experimental data in front of the plane; - - - - - - - - -, the experimental data behind the plane.

The HE and SE data of the investigated mixtures were next analyzed in terms of Graph theory. For this purpose it was assumed that (i + k) or (j + k) mixtures formation involve processes; (1) formation of unlike in –kn or jn –kn contacts; (2) unlike contact formation then weakens in –kn or jn –kn interactions which leads to their depolymerisation to form their respective monomers; and (3) monomers of i, j and k undergo specific interactions to form i:k or j:k molecular complex. If ik , jk , ii , jj , kk and 12 are molar interactions and

100

Neeti et al. / Thermochimica Acta 524 (2011) 92–103

Table 5 Measured densities, ; excess molar volumes, VE ; speeds of sound, u; isentropic compressibilities, S and excess isentropic compressibilities, SE data compared with Graph theory for the various (i + j + k) mixtures as a function of mole fraction, xi , of component (i) and xj , of component (j) at a temperature of 298.15, 303.15 and 308.15 K. xi

xj

ijk /kg m−3

u/m s−1

VE (Exptl.)/cm3 mol−1

o-toluidine (i) + tetrahydropyran (j) + N-methylformamide (k) T = 298.15 Ka 0.1093 0.7213 910.408 1335.90 −0.3656 0.1254 0.7001 913.084 1342.65 −0.3755 0.1448 0.6782 915.874 1349.72 −0.3773 0.6503 919.239 1358.08 −0.3746 0.1659 0.6212 922.649 1366.84 −0.3813 0.1822 0.6011 925.149 1373.05 −0.3626 0.2043 0.5501 931.399 1389.86 −0.3572 0.2457 0.5347 933.275 1394.20 −0.3306 0.2665 0.2826 0.4452 945.635 1436.27 −0.5887 0.3018 0.4426 946.019 1437.95 −0.5564 0.3982 952.375 1459.53 −0.6391 0.3329 0.4266 947.664 1439.91 −0.4155 0.3652 0.4023 951.651 1457.15 −0.5688 0.3564 0.4477 944.118 1423.21 −0.2694 0.3703 0.4124 949.112 1441.33 −0.3387 0.4008 0.3888 952.521 1454.20 −0.3914 0.4216 0.3851 952.035 1445.19 −0.2365 0.4582 0.3576 956.216 1463.08 −0.3329 0.4787 0.5025 0.3343 959.569 1476.41 −0.3851 0.3136 962.536 1486.28 −0.4315 0.5236 0.5458 0.3089 962.661 1485.41 −0.3644 0.2872 965.488 1495.46 −0.3788 0.5765 0.2671 968.484 1509.23 −0.4485 0.5903 0.6266 0.2348 972.697 1525.56 −0.4869 0.2137 975.337 1535.45 −0.5031 0.6499 0.6676 0.2035 976.410 1538.71 −0.4871 0.1913 977.915 1543.95 −0.4975 0.6782 0.1874 978.174 1544.26 −0.4733 0.6912 0.7143 0.1667 980.501 1551.86 −0.4674 0.7328 0.1766 978.767 1543.81 −0.3924 b T = 303.15 K 0.1093 0.7213 906.256 1312.75 −0.4524 0.1254 0.7001 909.129 1319.75 −0.4801 0.6782 912.177 1327.50 −0.5056 0.1448 0.6503 915.822 1336.49 −0.5279 0.1659 0.1822 0.6212 919.451 1345.12 −0.5528 0.2043 0.6011 922.224 1352.72 −0.5591 0.2457 0.5501 928.896 1370.34 −0.5891 0.5347 931.011 1376.54 −0.5836 0.2665 0.2826 0.4452 942.558 1405.82 −0.7501 0.3018 0.4426 943.164 1409.2 −0.7392 0.3329 0.3982 949.282 1427.27 −0.7939 0.4266 945.481 1419.35 −0.6642 0.3652 0.4023 948.879 1428.38 −0.7557 0.3564 0.3703 0.4477 942.443 1410.37 −0.5729 0.4352 947.211 1425.28 −0.6151 0.4008 0.3888 950.435 1435.66 −0.6466 0.4216 0.3851 950.446 1435.50 −0.5437 0.4582 0.3576 954.225 1448.27 −0.5958 0.4787 0.5025 0.3343 957.317 1458.83 −0.6192 0.3136 960.049 1468.37 −0.6397 0.5236 0.3089 960.322 1469.07 −0.5879 0.5458 0.2872 962.952 1478.52 −0.5803 0.5765 0.2671 965.637 1487.96 −0.6161 0.5903 0.6266 0.2348 969.521 1501.54 −0.6176 0.2137 971.959 1509.87 −0.6109 0.6499 0.2035 972.994 1513.43 −0.5898 0.6676 0.1913 974.390 1517.99 −0.5877 0.6782 0.1874 974.650 1519.32 −0.5632 0.6912 0.1667 976.858 1526.50 −0.5426 0.7143 0.1766 975.268 1522.03 −0.4834 0.7328 T = 308.15 Kc 0.1093 0.7213 901.282 1292.67 −0.4581 0.7001 904.289 1300.01 −0.4978 0.1254 0.6782 907.498 1308.17 −0.5377 0.1448 0.6503 911.22 1317.71 −0.5653 0.1659 0.6212 915.031 1326.54 −0.6061 0.1822 0.6011 918.04 1334.84 −0.6339 0.2043 0.5501 924.964 1353.16 −0.6838 0.2457 0.5347 927.272 1359.85 −0.6969 0.2665 0.4452 937.836 1385.81 −0.7581 0.2826 0.4426 938.641 1389.64 −0.7654 0.3018 0.3982 944.496 1406.84 −0.7906 0.3329

VE (Graph)/cm3 mol−1

(S )ijk /TPa

−1

(SE )ijk (Exptl/TPa−1 )

(SE )ijk (Graph)/TPa−1

−0.4078 −0.3925 −0.3662 −0.3580 −0.3817 −0.3533 −0.3633 −0.3394 −0.5730 −0.5348 −0.5934 −0.4159 −0.5285 −0.3099 −0.3606 −0.3973 −0.2836 −0.3501 −0.3874 −0.4176 −0.3588 −0.3607 −0.4239 −0.4686 −0.4996 −0.4875 −0.5172 −0.4850 −0.5124 −0.3539

615.48 607.52 599.34 589.83 580.13 573.34 555.81 551.24 512.63 511.22 492.91 508.95 494.89 522.92 507.18 496.45 502.92 488.55 478.11 470.30 470.80 463.13 453.31 441.74 434.89 432.57 428.98 428.69 423.50 428.68

−18.81 −20.61 −22.16 −23.58 −25.38 −25.67 −28.13 −27.34 −44.96 −43.95 −49.62 −36.62 −46.25 −26.74 −31.87 −35.46 −24.65 −31.07 −34.16 −35.42 −31.76 −31.75 −35.87 −36.92 −36.94 −35.33 −35.25 −33.43 −31.91 −27.08

−18.31 −19.70 −20.89 −22.76 −25.35 −26.08 −29.56 −29.65 −42.08 −40.97 −45.10 −36.66 −42.30 −31.35 −34.09 −35.98 −29.52 −32.73 −34.12 −36.69 −31.42 −30.48 −33.80 −35.36 −36.60 −35.29 −36.95 −34.45 −35.74 −24.34

−0.4725 −0.4873 −0.4973 −0.5183 −0.5522 −0.5551 −0.5932 −0.5899 −0.7417 −0.7249 −0.7651 −0.6636 −0.7301 −0.5991 −0.6295 −0.6493 −0.5724 −0.6072 −0.6197 −0.6309 −0.5847 −0.5696 −0.6004 −0.6054 −0.6089 −0.5893 −0.6001 −0.5708 −0.5706 −0.4566

640.31 631.53 622.09 611.30 601.11 592.58 573.29 566.85 536.82 533.91 517.12 525.01 516.54 533.43 519.71 510.48 510.58 499.63 490.83 483.11 482.50 475.05 467.74 457.48 451.31 448.71 445.38 444.48 439.32 442.62

−19.65 −21.91 −24.35 −26.56 −28.36 −30.05 −33.40 −34.24 −41.65 −42.13 −45.51 −41.26 −44.84 −37.33 −39.86 −41.55 −37.11 −39.64 −40.69 −41.55 −38.94 −38.37 −39.64 −38.85 −37.84 −36.36 −35.81 −34.56 −32.66 −29.94

−19.09 −21.28 −23.62 −26.17 −28.39 −30.34 −34.20 −35.37 −40.04 −40.58 −42.96 −41.22 −42.82 −39.51 −40.92 −41.75 −39.43 −40.48 −40.73 −40.90 −39.06 −37.74 −38.63 −38.03 −37.64 −36.39 −36.61 −35.01 −34.46 −28.69

−0.4701 −0.5024 −0.5350 −0.5760 −0.6067 −0.6312 −0.6829 −0.6958 −0.7583 −0.7621 −0.7833

663.99 654.33 643.91 632.03 621.04 611.34 590.44 583.19 555.22 551.69 534.95

−22.32 −25.05 −28.04 −30.81 −32.83 −35.31 −39.27 −40.61 −44.28 −45.31 −47.78

−21.51 −24.33 −27.45 −30.58 −32.86 −35.52 −39.82 −41.51 −43.07 −44.28 −45.85

Neeti et al. / Thermochimica Acta 524 (2011) 92–103

101

Table 5 (Continued ) xi

xj

ijk /kg m−3

u/m s−1

VE (Exptl.)/cm3 mol−1

VE (Graph)/cm3 mol−1

(S )ijk /TPa

(SE )ijk (Exptl/TPa−1 )

(SE )ijk (Graph)/TPa−1

0.3652 0.3564 0.3703 0.4008 0.4216 0.4582 0.4787 0.5025 0.5236 0.5458 0.5765 0.5903 0.6266 0.6499 0.6676 0.6782 0.6912 0.7143 0.7328

0.4266 0.4023 0.4477 0.4352 0.3888 0.3851 0.3576 0.3343 0.3136 0.3089 0.2872 0.2671 0.2348 0.2137 0.2035 0.1913 0.1874 0.1667 0.1766

941.709 944.443 939.286 943.945 946.827 947.484 950.902 953.78 956.287 956.818 959.365 961.735 965.39 967.712 968.746 970.095 970.4 972.552 971.193

1402.34 1408.91 1395.59 1409.62 1419.14 1421.83 1433.05 1442.65 1451.12 1453.04 1461.74 1468.88 1482.23 1489.96 1493.53 1497.85 1499.26 1507.71 1502.78

−0.7611 −0.7855 −0.7338 −0.7609 −0.7555 −0.7176 −0.7299 −0.7289 −0.7244 −0.6982 −0.6796 −0.6809 −0.6551 −0.6339 −0.6112 −0.6028 −0.5821 −0.5531 −0.5182

−0.7604 −0.7794 −0.7386 −0.7515 −0.7573 −0.7251 −0.7321 −0.7282 −0.7230 −0.6967 −0.6739 −0.6755 −0.6510 −0.6333 −0.6119 −0.6058 −0.5845 −0.5621 −0.5044

539.98 533.4 546.62 533.15 524.42 522.07 512.09 503.77 496.6 495.02 487.84 481.91 471.48 465.49 462.77 459.46 458.45 452.33 455.93

−46.88 −48.12 −45.12 −46.69 −47.43 −45.33 −46.36 −46.47 −46.36 −44.62 −43.34 −42.83 −41.57 −39.97 −38.40 −37.59 −36.36 −35.01 −32.15

−46.83 −46.76 −46.61 −47.33 −47.61 −46.82 −46.83 −46.42 −45.93 −44.63 −43.12 −43.43 −41.06 −39.80 −38.43 −37.96 −36.64 −35.14 −31.60

a

V(0) = −3.5554; V(1) = −8.4779; V(2) = 1768.07; ( (VE ) = 0.0004 cm3 mol −1

−1

−1

−1

S = −715.54; S = −3919.32; S = 129694.72 (SE ) = 0.04 TPa−1 * = −1.7656 cm3 mol−1 ;

−1

(0)

(1)

(2)

mol ; = −1.9412 cm mol ; = −3.7267 cm mol  = 119.17 TPa ; ∗ij = 48.75 TPa−1 ; ∗jk = −134.41 TPa−1 ; ∗ik = −298.01 TPa−1 . (0) (1) (2) V = −6.2034; V(1) = −7.5072; V(2) = 1037.6708; ( (VE ) = 0.0006 cm3 mol −1 S = −462.75; S = −1227.90; S = 56352.32 (SE ) = 0.04 TPa−1 * = 0.4688 cm3 mol−1 ; −1 −1 −1 ∗ij = 0.6967cm3 mol ; ∗jk = −1.6874 cm3 mol ; ∗ik = −2.9540 cm3 mol * = 62.89 TPa−1 ; ∗ij = −48.60 TPa−1 ; ∗jk = −50.68 TPa−1 ; ∗ik = −184.81 TPa−1 . (0) (1) (2) c V(0) = −4.5961; V(1) = −1.1855; V(2) = 311.7890; ( (VE ) = 0.0007cm3 mol −1 S = −403.05; S = −494.80; S = 30483.79 (SE ) = 0.05 TPa−1 ␹* = −0.1533 cm3 mol−1 ; −1 −1 −1 ∗ij = −0.8511 cm3 mol ; ∗jk = −0.9630 cm3 mol ; ∗ik = −1.8801 cm3 mol ␹* = 61.43 TPa−1 ; ∗ij = −104.09 TPa−1 ; ∗jk = −29.08 TPa−1 ; ∗ik = −139.23 TPa−1 . ∗ij = 2.8378 cm3 b (0)

∗jk

3

∗ik

3

E Fig. 5. Excess molar volumes, Vijk , for o-toluidine (i) + tetrahydropyran (j) + N-

methyl formamide (k) ternary mixture at 303.15 K, , the experimental data in front of the plane; - - - - - - - - -, the experimental data behind the plane.

molar compressibility interactions parameters for i–k, j–k, i–i, j–j, k–k contacts and specific interactions respectively, then change in molar thermodynamic properties, XE (X = H or S ) due to processes {1, 2 and 3} for (i + k) and (j + k) mixtures would be given [24–27] by Eqs. (11) and (12) respectively

 XE =

xi + xk

 E

X =

   xi xk 3 i /3 k   [ik + xi ii + xi kk + xk 12 ]

xj xk

3  /3  i k

3 3     j / k   jk + xj jj + xj kk + xk 12

xj + xk

3  /3  j k

−1

*

E Fig. 6. Excess molar volumes, Vijk , for o-toluidine (i) + tetrahydropyran (j) + N-

methyl formamide (k) ternary mixture at 308.15 K, , the experimental data in front of the plane; - - - - - - - - -, the experimental data behind the plane.

For the studied mixtures, it is reasonable to assume that ik ∼ = / / 12 = ik ; ii = kk = ∗ , jk ∼ = 12 = jk ; jj = kk = ∗ then Eqs. (11) and (12) can be expressed by



XE =

X = (11)

(12)

3 3    i / k   (1 + xk ) /ik + 2xi ∗

(13)

3 3    j / k   (1 + xk ) /jk + 2xj ∗

(14)

xi + xk

 E

xi xk

xj xk

xj + xk

3  /3  i k

3  /3  j k

Eqs. (13) and (14) contain two unknown parameters and were determined by employing HE and SE data of the studied mixtures at xi = 0.4 and 0.6. These parameters were then utilized to determine HE and SE values of mixtures at other values of xi . Such HE and SE /

/

values along with ik , jk and ∗ parameters are recorded in Table 4.

102

Neeti et al. / Thermochimica Acta 524 (2011) 92–103

Fig. 9. Isentropic compressibilities, (SE )ijk for o-toluidine (i) + tetrahydropyran (j) + N-methyl formamide (k) ternary mixture at 308.15 K, , the experimental data in front of the plane; - - - - - - - - -, the experimental data behind the plane. Fig. 7. Isentropic compressibilities, (SE )ijk for o-toluidine (i) + tetrahydropyran (j) + N-methyl formamide (k) ternary mixture at 298.15 K, , the experimental data in front of the plane; - - - - - - - - -, the experimental data behind the plane.

like NMF (k) is added to OT (i) + THP (j) mixture then ternary OT (i) + THP (j) + NMF (k) mixture formation may be assumed to involve processes; (1) establishment of unlike (a) in –jn , jn –kn , in –kn contacts; (2) unlike contact formation leads to depolymerisation of in , jn , kn to form their monomers; and (3) monomers of i, j and k then undergo specific interactions to form (a) i:j (b) j:k and (c) i:k molec/ / / / // ular complexes. If ij , jk , ik ; ii , jj , kk ; and 12 , 12 , 12 are the molar volumes and molar compressibilities interaction parameters for in –jn , jn –kn , in –kn contacts; depolymerisation of in , jn , kn ; and specific interactions between i:j; j:k and i:k components of the ternary mixtures then change in thermodynamic properties, X (X = V or S ) due to processes 1 (a)–(c), (2) (a)–(b) and (3) (a)–(c) is given by [24–27]



E Xijk

(X = V or S )

=

xi xj

3 3    i / j   ij + xi /ii + xj 12

xi + xj

 +

 +

3  /3  i j

    xj xk 3 j /3 k   jk + xj /jj + xk /12

xj + xk xk xi

3  /3  j k

3 3    k / i   ik + xk /kk + xi // 12

xk + xi

3  /3  k i

(15) Fig. 8. Isentropic compressibilities,

(SE )ijk

for o-toluidine (i) + tetrahydropyran

(j) + N-methyl formamide (k) ternary mixture at 303.15 K, , the experimental data in front of the plane; - - - - - - - - -, the experimental data behind the plane.

For the present (i + j + k) mixture, if it is assumed that; ij ∼ = 12 = ∼ / = ∗ ; ii = jj = kk = ∗ then Eq. (15) reduces to jk =

∗ij ;

E (X Xijk

12

= V or S )

jk



=

xi xj

3 3    i / j   (1 + xj )xij∗ + xi x∗

xi + xj

3  /3  i j

Examination of data in Table 4 reveals that HE and SE values differ by maximum of 1 and 6% respectively with their experimental values. This gives additional support to the various assumptions made in deriving Eqs. (13) and (14).

−8pt

+

5.3. Excess molar volumes and excess isentropic compressibilities of ternary mixtures

−8pt

+

Topological analysis of VE , HE and SE data of (i + k) or (j + k) mixtures has revealed that OT (i) or THP (j) or NMF (k) exists as associated molecular entities, in , jn , kn respectively. If a component

Eq. (16) has four unknown ∗ij etc. parameters and for the present analysis, we utilized the observed data at four arbitrary compositions to evaluate them. These parameters were then used to



xj xk (3 j /3 k )



xj + xk (3 j /3 k )



xk xi (3 k /3 i ) xk + xi (3 k /3 i )







(1 + xk )∗jk + xj ∗ (16)

(1 + xi ) ∗ik + xk ∗



Neeti et al. / Thermochimica Acta 524 (2011) 92–103 E (X = V or  ) data of the investigated mixtures at other evaluate Xijk S E Xijk

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